genetic algorithm.pdf
TRANSCRIPT
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IntroductionAlgorithm
TheoryWhy GA?
Applications
Genetic Algorithm
Saif Hasan Sagar Chordia Rahul Varshneya
February 6, 2012
GuidePushpak Bhattacharyya
1 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
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IntroductionAlgorithm
TheoryWhy GA?
Applications
IntroductionHistoryMotivationTerminology
INTRODUCTION
2 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
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IntroductionAlgorithm
TheoryWhy GA?
Applications
IntroductionHistoryMotivationTerminology
Introduction
Genetic algorithms are a family of computational modelsbelonging to the class of evolutionary algorithms, part of
artificial intelligence
3 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
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IntroductionAlgorithm
TheoryWhy GA?
Applications
IntroductionHistoryMotivationTerminology
Introduction
Genetic algorithms are a family of computational modelsbelonging to the class of evolutionary algorithms, part of
artificial intelligence
These algorithms encode a potential solution to a specificproblem on a simple chromosome like data structure
3 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
I d i
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IntroductionAlgorithm
TheoryWhy GA?
Applications
IntroductionHistoryMotivationTerminology
Introduction
Genetic algorithms are a family of computational modelsbelonging to the class of evolutionary algorithms, part of
artificial intelligence
These algorithms encode a potential solution to a specificproblem on a simple chromosome like data structure
Uses techniques inspired by natural evolution such as
inheritance, mutation, selection and crossover
3 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
I t d ti
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IntroductionAlgorithm
TheoryWhy GA?
Applications
IntroductionHistoryMotivationTerminology
Introduction
Genetic algorithms are a family of computational modelsbelonging to the class of evolutionary algorithms, part of
artificial intelligenceThese algorithms encode a potential solution to a specificproblem on a simple chromosome like data structure
Uses techniques inspired by natural evolution such as
inheritance, mutation, selection and crossoverThey are often viewed as function optimizers
3 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
Introduction
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IntroductionAlgorithm
TheoryWhy GA?
Applications
IntroductionHistoryMotivationTerminology
History
First appeared in 1950s and early 1960s while biologists wereexplicitly seeking to the model of natural evolution
4 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
Introduction
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IntroductionAlgorithm
TheoryWhy GA?
Applications
IntroductionHistoryMotivationTerminology
History
First appeared in 1950s and early 1960s while biologists wereexplicitly seeking to the model of natural evolution
Idea of inheritance and mutation introduced by Ingo
Rechenberg which is termed as evolution strategy (1965)
4 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
Introduction
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IntroductionAlgorithm
TheoryWhy GA?
Applications
IntroductionHistoryMotivationTerminology
History
First appeared in 1950s and early 1960s while biologists wereexplicitly seeking to the model of natural evolution
Idea of inheritance and mutation introduced by Ingo
Rechenberg which is termed as evolution strategy (1965)M.J. Walsh introduced evolutionary programming (1966)
4 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionI d i
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IntroductionAlgorithm
TheoryWhy GA?
Applications
IntroductionHistoryMotivationTerminology
History
First appeared in 1950s and early 1960s while biologists wereexplicitly seeking to the model of natural evolution
Idea of inheritance and mutation introduced by Ingo
Rechenberg which is termed as evolution strategy (1965)M.J. Walsh introduced evolutionary programming (1966)
Later versions introduced population which leads to theGenetic Algorithms
4 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionI t d ti
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AlgorithmTheory
Why GA?Applications
IntroductionHistoryMotivationTerminology
History
First appeared in 1950s and early 1960s while biologists wereexplicitly seeking to the model of natural evolution
Idea of inheritance and mutation introduced by Ingo
Rechenberg which is termed as evolution strategy (1965)M.J. Walsh introduced evolutionary programming (1966)
Later versions introduced population which leads to theGenetic Algorithms
In 1975 John Holland published book Adaptation in Naturaland Artificial System. This was the first book to representconcept of adaptive digital systems using mutation, selectionand crossover.
4 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionIntroduction
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AlgorithmTheory
Why GA?Applications
IntroductionHistoryMotivationTerminology
Motivation
Evolution is very powerful theory since biological principles likecommon descent and selective breeding have been used forthe benefit of humans
5 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
Introduction Introduction
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AlgorithmTheory
Why GA?Applications
IntroductionHistoryMotivationTerminology
Motivation
Evolution is very powerful theory since biological principles likecommon descent and selective breeding have been used forthe benefit of humans
Living organisms are consummate problem solvers. Theyexhibit a versatility that puts the best computer programs toshame.
5 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
Introduction Introduction
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AlgorithmTheory
Why GA?Applications
IntroductionHistoryMotivationTerminology
Motivation
Evolution is very powerful theory since biological principles likecommon descent and selective breeding have been used forthe benefit of humans
Living organisms are consummate problem solvers. Theyexhibit a versatility that puts the best computer programs toshame.
Most organisms evolve by means of two primary processes:
natural selection and sexual reproduction. The first determineswhich members of population survive and reproduce, and thesecond ensures mixing and recombination among the genes of their offspring. Similar analogy is used in GA.
5 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAl i h
Introduction
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AlgorithmTheory
Why GA?Applications
IntroductionHistoryMotivationTerminology
Terminology
Search space/ State space : the space of all feasible solutions.
6 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAl ith
Introduction
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AlgorithmTheory
Why GA?Applications
HistoryMotivationTerminology
Terminology
Search space/ State space : the space of all feasible solutions.
Chromosome : a set of genes; a chromosome contains the
solution in form of genes.
6 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Introduction
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AlgorithmTheory
Why GA?Applications
HistoryMotivationTerminology
Terminology
Search space/ State space : the space of all feasible solutions.
Chromosome : a set of genes; a chromosome contains the
solution in form of genes.Population : a set of solutions (or individuals/chromosomes).
6 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Introduction
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AlgorithmTheory
Why GA?Applications
HistoryMotivationTerminology
Terminology
Search space/ State space : the space of all feasible solutions.
Chromosome : a set of genes; a chromosome contains the
solution in form of genes.Population : a set of solutions (or individuals/chromosomes).
Generation : the process of evaluation, selection,recombination and mutation.
6 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
IntroductionHi
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AlgorithmTheory
Why GA?Applications
HistoryMotivationTerminology
Terminology
Search space/ State space : the space of all feasible solutions.
Chromosome : a set of genes; a chromosome contains the
solution in form of genes.Population : a set of solutions (or individuals/chromosomes).
Generation : the process of evaluation, selection,recombination and mutation.
Fitness : the value assigned to an individual based on how faror close it is from the solution; greater the fitness value betterthe solution it contains.
6 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
AlgorithmE di
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AlgorithmTheory
Why GA?Applications
EncodingOperations of GAParameters of GA
ALGORITHM
7 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
AlgorithmEncoding
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gTheory
Why GA?Applications
EncodingOperations of GAParameters of GA
Algorithm
Psuedocode of Genetics Algorithm
8 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
AlgorithmEncoding
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TheoryWhy GA?
Applications
EncodingOperations of GAParameters of GA
Algorithm
Psuedocode of Genetics Algorithm
Choose the initial population of individuals
8 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
AlgorithmEncoding
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TheoryWhy GA?
Applications
EncodingOperations of GAParameters of GA
Algorithm
Psuedocode of Genetics Algorithm
Choose the initial population of individuals
Evaluate the fitness of each individual in population
8 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Th
AlgorithmEncoding
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TheoryWhy GA?
Applications
EncodingOperations of GAParameters of GA
Algorithm
Psuedocode of Genetics Algorithm
Choose the initial population of individuals
Evaluate the fitness of each individual in populationRepeat until termination condition satisfied:
8 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Th
AlgorithmEncoding
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TheoryWhy GA?
Applications
gOperations of GAParameters of GA
Algorithm
Psuedocode of Genetics Algorithm
Choose the initial population of individuals
Evaluate the fitness of each individual in populationRepeat until termination condition satisfied:
Selection: Select the individuals with greater fitness forreproduction
8 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
AlgorithmEncoding
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TheoryWhy GA?
Applications
gOperations of GAParameters of GA
Algorithm
Psuedocode of Genetics Algorithm
Choose the initial population of individuals
Evaluate the fitness of each individual in populationRepeat until termination condition satisfied:
Selection: Select the individuals with greater fitness forreproductionCrossover: Breed new individuals through crossover
8 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
AlgorithmEncoding
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TheoryWhy GA?
Applications
Operations of GAParameters of GA
Algorithm
Psuedocode of Genetics Algorithm
Choose the initial population of individuals
Evaluate the fitness of each individual in populationRepeat until termination condition satisfied:
Selection: Select the individuals with greater fitness forreproductionCrossover: Breed new individuals through crossover
Mutation: Apply probabilistic mutation on new individuals
8 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
AlgorithmEncodingO f G
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TheoryWhy GA?
Applications
Operations of GAParameters of GA
Algorithm
Psuedocode of Genetics Algorithm
Choose the initial population of individuals
Evaluate the fitness of each individual in populationRepeat until termination condition satisfied:
Selection: Select the individuals with greater fitness forreproductionCrossover: Breed new individuals through crossover
Mutation: Apply probabilistic mutation on new individualsForm a new population with these offsprings.
8 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
AlgorithmEncodingO i f GA
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TheoryWhy GA?
Applications
Operations of GAParameters of GA
Algorithm
Psuedocode of Genetics Algorithm
Choose the initial population of individuals
Evaluate the fitness of each individual in population
Repeat until termination condition satisfied:
Selection: Select the individuals with greater fitness forreproductionCrossover: Breed new individuals through crossover
Mutation: Apply probabilistic mutation on new individualsForm a new population with these offsprings.
Terminate
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IntroductionAlgorithm
Theory
AlgorithmEncodingO ti f GA
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yWhy GA?
Applications
Operations of GAParameters of GA
Flow Chart
9 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
AlgorithmEncodingOperations of GA
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yWhy GA?
Applications
Operations of GAParameters of GA
Encoding
Before a genetic algorithm can be put to work on any problem, amethod is needed to encode potential solutions to that problem ina form so that a computer can process.
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IntroductionAlgorithm
Theory
AlgorithmEncodingOperations of GA
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Why GA?Applications
Operations of GAParameters of GA
Encoding
Before a genetic algorithm can be put to work on any problem, amethod is needed to encode potential solutions to that problem ina form so that a computer can process.
Common approaches are:
Binary Encoding : every chromosome is a string of 0 or 1
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IntroductionAlgorithmTheory
Wh GA?
AlgorithmEncodingOperations of GA
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Why GA?Applications
Operations of GAParameters of GA
Encoding
Before a genetic algorithm can be put to work on any problem, amethod is needed to encode potential solutions to that problem ina form so that a computer can process.
Common approaches are:
Binary Encoding : every chromosome is a string of 0 or 1
Permutation Encoding : every chromosome is a string of numbers that represent position in a sequence
10/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithmTheory
Wh GA?
AlgorithmEncodingOperations of GA
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Why GA?Applications
Operations of GAParameters of GA
Encoding
Before a genetic algorithm can be put to work on any problem, amethod is needed to encode potential solutions to that problem ina form so that a computer can process.
Common approaches are:
Binary Encoding : every chromosome is a string of 0 or 1
Permutation Encoding : every chromosome is a string of numbers that represent position in a sequence
Tree Encoding : a tree structure represents the chromosome
10/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithmTheory
Wh GA?
AlgorithmEncodingOperations of GA
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Why GA?Applications
pParameters of GA
Encoding
Before a genetic algorithm can be put to work on any problem, amethod is needed to encode potential solutions to that problem ina form so that a computer can process.
Common approaches are:
Binary Encoding : every chromosome is a string of 0 or 1
Permutation Encoding : every chromosome is a string of numbers that represent position in a sequence
Tree Encoding : a tree structure represents the chromosome
Value Encoding : every chromosome is a sequence of somevalues (real numbers, characters or objects)
10/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithmTheory
Why GA?
AlgorithmEncodingOperations of GA
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Why GA?Applications
Parameters of GA
Encoding Examples
Binary Encoding : Suppose we have a knapsack of capacity C and N items, then we can encode this problem as follows
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IntroductionAlgorithmTheory
Why GA?
AlgorithmEncodingOperations of GA
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Why GA?Applications
Parameters of GA
Encoding Examples
Binary Encoding : Suppose we have a knapsack of capacity C and N items, then we can encode this problem as follows
Chromosome, in this case, is a string of 0s and 1s with N bits
11/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithmTheory
Why GA?
AlgorithmEncodingOperations of GAP f GA
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Why GA?Applications
Parameters of GA
Encoding Examples
Binary Encoding : Suppose we have a knapsack of capacity C and N items, then we can encode this problem as follows
Chromosome, in this case, is a string of 0s and 1s with N bits
Represent item i of problem with i th
bit in the chromosome
11/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithmTheory
Why GA?
AlgorithmEncodingOperations of GAP t f GA
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y GApplications
Parameters of GA
Encoding Examples
Binary Encoding : Suppose we have a knapsack of capacity C and N items, then we can encode this problem as follows
Chromosome, in this case, is a string of 0s and 1s with N bits
Represent item i of problem with i th
bit in the chromosomei th bit is 1 iff i th item has been selected, 0 otherwise.
11/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithmTheory
Why GA?
AlgorithmEncodingOperations of GAParameters of GA
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yApplications
Parameters of GA
Encoding Examples
Binary Encoding : Suppose we have a knapsack of capacity C and N items, then we can encode this problem as follows
Chromosome, in this case, is a string of 0s and 1s with N bits
Represent item i of problem with i th
bit in the chromosomei th bit is 1 iff i th item has been selected, 0 otherwise.The set of all such chromosomes (2N ) is the solution space of the problem.
11/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithmTheory
Why GA?
AlgorithmEncodingOperations of GAParameters of GA
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ApplicationsParameters of GA
Encoding Examples
Binary Encoding : Suppose we have a knapsack of capacity C and N items, then we can encode this problem as follows
Chromosome, in this case, is a string of 0s and 1s with N bits
Represent item i of problem with i th
bit in the chromosomei th bit is 1 iff i th item has been selected, 0 otherwise.The set of all such chromosomes (2N ) is the solution space of the problem.
Chromosome 1: 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1
Chromosome 2: 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1The example shown above has 24 items (and therefore 24 bits)with item1 selected in both chromosome 1 and 2 whereasitem2 is selected in chromosome 2 but not in chromosome 1.
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IntroductionAlgorithmTheory
Why GA?
AlgorithmEncodingOperations of GAParameters of GA
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ApplicationsParameters of GA
Encoding Examples
Permutation Encoding : Travelling Salesman Problem
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IntroductionAlgorithmTheory
Why GA?A li i
AlgorithmEncodingOperations of GAParameters of GA
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ApplicationsParameters of GA
Encoding Examples
Permutation Encoding : Travelling Salesman Problem
Problem descripition : There are cities and given distancesbetween them. Travelling salesman has to visit all of them, but
he doesn’t want to travel more than necessary. Find asequence of cities with a minimal travelled distance.
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IntroductionAlgorithmTheory
Why GA?A li ti
AlgorithmEncodingOperations of GAParameters of GA
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Applications
Encoding Examples
Permutation Encoding : Travelling Salesman Problem
Problem descripition : There are cities and given distancesbetween them. Travelling salesman has to visit all of them, but
he doesn’t want to travel more than necessary. Find asequence of cities with a minimal travelled distance.
Chromosome A: 1 5 3 2 6 4 7 9 8
Chromosome B: 8 5 6 7 2 3 1 4 9
Encoding : Here, encoded chromosomes describe the order of
cities the salesman visits. For example, in chromosome A, thesalesman visits city-1 followed by city-5 followed by city-3 andso on.
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IntroductionAlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
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Applications
Encoding Examples
Tree Encoding : Genetic Programming
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IntroductionAlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
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Applications
Encoding Examples
Tree Encoding : Genetic Programming
In tree encoding, every chromosome is a tree of some objects,such as functions or commands in programming language.
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IntroductionAlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
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Applications
Encoding Examples
Tree Encoding : Genetic Programming
In tree encoding, every chromosome is a tree of some objects,such as functions or commands in programming language.Tree encoding is useful for evolving programs or any otherstructures that can be encoded in trees.
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IntroductionAlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
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Applications
Encoding Examples
Tree Encoding : Genetic Programming
In tree encoding, every chromosome is a tree of some objects,such as functions or commands in programming language.Tree encoding is useful for evolving programs or any otherstructures that can be encoded in trees.The crossover and mutation can be done relatively easy way .
13/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
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pp
Encoding Examples
Tree Encoding : Genetic Programming
In tree encoding, every chromosome is a tree of some objects,such as functions or commands in programming language.Tree encoding is useful for evolving programs or any otherstructures that can be encoded in trees.The crossover and mutation can be done relatively easy way .
Image courtesy: http://www.myreaders.info/09 Genetic Algorithms.pdf
13/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
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Operations of Genetic Algorithm
Genetic operators used in GA maintain genetic diversity.
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IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
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Operations of Genetic Algorithm
Genetic operators used in GA maintain genetic diversity.
Genetic diversity or variation is a necessity for evolution.
14/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
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Operations of Genetic Algorithm
Genetic operators used in GA maintain genetic diversity.
Genetic diversity or variation is a necessity for evolution.Genetic operators are analogous to those which occur in thenatural world:
14/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
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Operations of Genetic Algorithm
Genetic operators used in GA maintain genetic diversity.
Genetic diversity or variation is a necessity for evolution.
Genetic operators are analogous to those which occur in thenatural world:
Reproduction (or Selection)
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IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
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Operations of Genetic Algorithm
Genetic operators used in GA maintain genetic diversity.
Genetic diversity or variation is a necessity for evolution.
Genetic operators are analogous to those which occur in thenatural world:
Reproduction (or Selection)Crossover (or Recombination)
14/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
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Operations of Genetic Algorithm
Genetic operators used in GA maintain genetic diversity.
Genetic diversity or variation is a necessity for evolution.
Genetic operators are analogous to those which occur in thenatural world:
Reproduction (or Selection)Crossover (or Recombination)
Mutation
14/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
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Reproduction or Selection
Concept : From the population, the chromosomes are selectedto be parents to crossover and produce offspring.
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IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
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Reproduction or Selection
Concept : From the population, the chromosomes are selectedto be parents to crossover and produce offspring.
Problem : How to select these chromosomes ?
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
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Reproduction or Selection
Concept : From the population, the chromosomes are selectedto be parents to crossover and produce offspring.
Problem : How to select these chromosomes ?
Hint : According to Charles Darwin’s evolution theory”survival of the fittest” - the best ones should survive andcreate new offspring.
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
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Reproduction or Selection
Concept : From the population, the chromosomes are selectedto be parents to crossover and produce offspring.
Problem : How to select these chromosomes ?
Hint : According to Charles Darwin’s evolution theory”survival of the fittest” - the best ones should survive andcreate new offspring.
Solution : Fitness function quantifies the optimality of a
solution (chromosome) so that a particular solution may beranked against all the other solutions. The function depictsthe closeness of a given ’solution’ to the desired result.
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
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Reproduction or Selection
Popular methods of selection include :
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
R d i S l i
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Reproduction or Selection
Popular methods of selection include :
Roulette-wheel selection
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
R d i S l i
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Reproduction or Selection
Popular methods of selection include :
Roulette-wheel selection
Tournament selection
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
R d i S l i
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Reproduction or Selection
Popular methods of selection include :
Roulette-wheel selection
Tournament selectionRank selection
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
R d ti S l ti
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Reproduction or Selection
Popular methods of selection include :
Roulette-wheel selection
Tournament selectionRank selection
Steady-state selection
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
R d ti S l ti
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Reproduction or Selection
Popular methods of selection include :
Roulette-wheel selection
Tournament selectionRank selection
Steady-state selection
Boltzmann selection
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
Reproduction or Selection
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Reproduction or Selection
Popular methods of selection include :
Roulette-wheel selection
Tournament selectionRank selection
Steady-state selection
Boltzmann selection
Scaling selection
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
Roulette Wheel Selection
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Roulette-Wheel Selection
Concept : the chance of an individual’s being selected isproportional to its fitness, greater or less than its competitors’fitness.
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
Roulette Wheel Selection
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Roulette-Wheel Selection
Concept : the chance of an individual’s being selected isproportional to its fitness, greater or less than its competitors’fitness.
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
Roulette Wheel Selection
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Roulette-Wheel Selection
Concept : the chance of an individual’s being selected isproportional to its fitness, greater or less than its competitors’fitness.
Implementation : Probability of selection of i th individual is:p i = f i
ΣN j =1f j
where f i :fitness of i th individual, N : number of individuals
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
Elitist Selection
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Elitist Selection
Concept : Most fit members of each generation areguaranteed to be selected for next generation.
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
Elitist Selection
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Elitist Selection
Concept : Most fit members of each generation areguaranteed to be selected for next generation.
Advantages :
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Introduction
AlgorithmTheory
Why GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
Elitist Selection
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Elitist Selection
Concept : Most fit members of each generation areguaranteed to be selected for next generation.
Advantages :Ensures that the best solution found so far is not lost due tocrossover and mutation.
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Introduction
AlgorithmTheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
Elitist Selection
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Elitist Selection
Concept : Most fit members of each generation areguaranteed to be selected for next generation.
Advantages :Ensures that the best solution found so far is not lost due tocrossover and mutation.Speeds up convergence once a good solution has beendiscovered.
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Introduction
AlgorithmTheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
Crossover
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Crossover
Concept : Selects genes from parent chromosomes, combinesthem and creates a new offspring.
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Introduction
AlgorithmTheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
Crossover
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Crossover
Concept : Selects genes from parent chromosomes, combinesthem and creates a new offspring.
Idea : New chromosome may be better than both of theparents if it takes the best characteristics from each of them
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Introduction
AlgorithmTheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
Crossover
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Concept : Selects genes from parent chromosomes, combinesthem and creates a new offspring.
Idea : New chromosome may be better than both of theparents if it takes the best characteristics from each of them
Consider the two parents selected for crossover.
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Introduction
AlgorithmTheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
Crossover
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Concept : Selects genes from parent chromosomes, combinesthem and creates a new offspring.
Idea : New chromosome may be better than both of theparents if it takes the best characteristics from each of them
Consider the two parents selected for crossover.
Interchange the parents chromosomes after crossover points.The offsprings produced are :
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Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover
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The Crossover operators are of many types.
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Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover
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The Crossover operators are of many types.
Single-Point crossover
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Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover
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The Crossover operators are of many types.
Single-Point crossoverTwo Point crossover
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Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover
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The Crossover operators are of many types.
Single-Point crossoverTwo Point crossoverUniform crossover
20/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover
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The Crossover operators are of many types.
Single-Point crossoverTwo Point crossoverUniform crossoverArithmetic crossover
20/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover
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The Crossover operators are of many types.
Single-Point crossoverTwo Point crossoverUniform crossoverArithmetic crossover
Which Crossover operator is to be selected is based onchromosome encoding
20/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover
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The Crossover operators are of many types.
Single-Point crossoverTwo Point crossoverUniform crossoverArithmetic crossover
Which Crossover operator is to be selected is based onchromosome encoding
Specific crossover made for a specific problem can improveperformance of the genetic algorithm
20/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover
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The Crossover operators are of many types.
Single-Point crossoverTwo Point crossoverUniform crossoverArithmetic crossover
Which Crossover operator is to be selected is based onchromosome encoding
Specific crossover made for a specific problem can improveperformance of the genetic algorithm
Some research suggests more than two “parents” are better toreproduce a good quality chromosome (Eiben, A.E. et al (1994),
Ting, Chuan-Kang (2005))
20/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Two-Point Crossover
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Operation : randomly select two crossover points within achromosome, then interchange the two parent chromosomesbetween these points to produce two new offspring.Consider the two parents selected for crossover.
21/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Uniform Crossover
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Operation : mixing ratio decides the contribution of eachparent to the gene values in the offspring chromosomes.
Advantage : allows the parent chromosomes to be mixed atthe gene level rather than the segment level
Consider the two parents selected for crossover.
If the mixing ratio is 0.5 approximately, then the possible set of
offsprings after crossover would be :
Image courtesy: http://www.myreaders.info/09 Genetic Algorithms.pdf
22/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
Introduction
AlgorithmTheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Mutation
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Concept : Mutation alters one or more gene values in achromosome from its initial state.
23/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Mutation
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Concept : Mutation alters one or more gene values in achromosome from its initial state.
Advantages :
23/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Mutation
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Concept : Mutation alters one or more gene values in achromosome from its initial state.
Advantages :
Mutation can generate new genes values not already present in
sample space which can lead to better solution.
23/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Mutation
![Page 91: genetic algorithm.pdf](https://reader030.vdocument.in/reader030/viewer/2022020714/577cd6cb1a28ab9e789d4403/html5/thumbnails/91.jpg)
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Concept : Mutation alters one or more gene values in achromosome from its initial state.
Advantages :
Mutation can generate new genes values not already present in
sample space which can lead to better solution.Randomness introduced by mutation helps in searching forglobal optima solutions and not geting stuck in local optima.(premature convergence).
23/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Mutation
![Page 92: genetic algorithm.pdf](https://reader030.vdocument.in/reader030/viewer/2022020714/577cd6cb1a28ab9e789d4403/html5/thumbnails/92.jpg)
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Concept : Mutation alters one or more gene values in achromosome from its initial state.
Advantages :
Mutation can generate new genes values not already present in
sample space which can lead to better solution.Randomness introduced by mutation helps in searching forglobal optima solutions and not geting stuck in local optima.(premature convergence).
Operators : Mutation operators are of many type :
23/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Mutation
![Page 93: genetic algorithm.pdf](https://reader030.vdocument.in/reader030/viewer/2022020714/577cd6cb1a28ab9e789d4403/html5/thumbnails/93.jpg)
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Concept : Mutation alters one or more gene values in achromosome from its initial state.
Advantages :
Mutation can generate new genes values not already present in
sample space which can lead to better solution.Randomness introduced by mutation helps in searching forglobal optima solutions and not geting stuck in local optima.(premature convergence).
Operators : Mutation operators are of many type :
one simple way is, Flip Bit.
23/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Mutation
![Page 94: genetic algorithm.pdf](https://reader030.vdocument.in/reader030/viewer/2022020714/577cd6cb1a28ab9e789d4403/html5/thumbnails/94.jpg)
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Concept : Mutation alters one or more gene values in achromosome from its initial state.
Advantages :
Mutation can generate new genes values not already present in
sample space which can lead to better solution.Randomness introduced by mutation helps in searching forglobal optima solutions and not geting stuck in local optima.(premature convergence).
Operators : Mutation operators are of many type :
one simple way is, Flip Bit.the others are Boundary, Uniform, and Gaussian.
23/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Mutation
![Page 95: genetic algorithm.pdf](https://reader030.vdocument.in/reader030/viewer/2022020714/577cd6cb1a28ab9e789d4403/html5/thumbnails/95.jpg)
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Concept : Mutation alters one or more gene values in achromosome from its initial state.
Advantages :
Mutation can generate new genes values not already present in
sample space which can lead to better solution.Randomness introduced by mutation helps in searching forglobal optima solutions and not geting stuck in local optima.(premature convergence).
Operators : Mutation operators are of many type :
one simple way is, Flip Bit.the others are Boundary, Uniform, and Gaussian.
Operators are selected based on encoding of chromosomes.
23/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Flip Bit
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The mutation operator simply inverts the value of the chosengene i.e. 0 goes to 1 and 1 goes to 0.
Consider the two original offsprings selected for mutation.
The Mutated Off-spring produced are :
Image courtesy: http://www.myreaders.info/09 Genetic Algorithms.pdf
24/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Parameters of Genetic Algorithm
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There are three basic parameters of Genetic Algorithm.
25/ 42 Saif Hasa Saga Cho dia Rah l Va sh e a Ge etic Algo ith
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Parameters of Genetic Algorithm
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There are three basic parameters of Genetic Algorithm.
Crossover Probability
25/ 42 S if H S Ch di R h l V h G ti Al ith
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Parameters of Genetic Algorithm
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There are three basic parameters of Genetic Algorithm.
Crossover ProbabilityMutation Probability
25/ 42 S if H S Ch di R h l V h G ti Al ith
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Parameters of Genetic Algorithm
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There are three basic parameters of Genetic Algorithm.
Crossover ProbabilityMutation Probability
Population Size
25/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover Probability
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Definition : Crossover probability represents how oftencrossover is performed.
26/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover Probability
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Definition : Crossover probability represents how oftencrossover is performed.
Constraint :
26/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover Probability
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Definition : Crossover probability represents how oftencrossover is performed.
Constraint :
If the crossover rate is too high, high performance strings are
eliminated faster than selection can produce improvements.
26/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover Probability
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Definition : Crossover probability represents how oftencrossover is performed.
Constraint :
If the crossover rate is too high, high performance strings are
eliminated faster than selection can produce improvements.A low crossover rate may cause stagnation due to the lowerexploration rate.
26/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover Probability
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Definition : Crossover probability represents how oftencrossover is performed.
Constraint :
If the crossover rate is too high, high performance strings are
eliminated faster than selection can produce improvements.A low crossover rate may cause stagnation due to the lowerexploration rate.
Solution : Crossover rate generally should be high, about80%-95%.
26/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Crossover Probability
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Definition : Crossover probability represents how oftencrossover is performed.
Constraint :
If the crossover rate is too high, high performance strings are
eliminated faster than selection can produce improvements.A low crossover rate may cause stagnation due to the lowerexploration rate.
Solution : Crossover rate generally should be high, about80%-95%.Some results show that for some problems crossover rateabout 60% is the best.
26/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Mutation Probability
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Defintion : Mutation probability represents how oftenmutation is performed.
27/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Algorithm
EncodingOperations of GAParameters of GA
Mutation Probability
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Defintion : Mutation probability represents how oftenmutation is performed.
Constraints :
27/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
Mutation Probability
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Defintion : Mutation probability represents how oftenmutation is performed.
Constraints :
A very small mutation rate may lead to convergence to localoptima areas.
27/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
Mutation Probability
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Defintion : Mutation probability represents how oftenmutation is performed.
Constraints :
A very small mutation rate may lead to convergence to localoptima areas.A mutation rate that is too high results in almost randomsearch.
27/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
Mutation Probability
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Defintion : Mutation probability represents how oftenmutation is performed.
Constraints :
A very small mutation rate may lead to convergence to localoptima areas.A mutation rate that is too high results in almost randomsearch.
Solution :Best rates reported are about 0.5%-1%.
27/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
Population Size
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Definition : Number of chromosomes in population (in onegeneration).
28/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
AlgorithmEncodingOperations of GAParameters of GA
Population Size
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Definition : Number of chromosomes in population (in onegeneration).
Constraints :
28/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
Population Size
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Definition : Number of chromosomes in population (in onegeneration).
Constraints :
Too few chromosomes implies GA have a few possibilities toperform crossover and only a small part of search space isexplored.
28/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
Population Size
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Definition : Number of chromosomes in population (in onegeneration).
Constraints :
Too few chromosomes implies GA have a few possibilities toperform crossover and only a small part of search space isexplored.Too many chromosomes implies GA slows down.
28/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
AlgorithmEncodingOperations of GAParameters of GA
Population Size
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Definition : Number of chromosomes in population (in onegeneration).
Constraints :
Too few chromosomes implies GA have a few possibilities toperform crossover and only a small part of search space isexplored.Too many chromosomes implies GA slows down.
Solution : Good population size is about 20-30, however
sometimes sizes 50-100 are reported as best.
28/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
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Why Genetic Algorithms Work?
29/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
Schema and HyperPlane
Schema - solution string with some blank fields
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geg: 01***********
30/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
Schema and HyperPlane
Schema - solution string with some blank fields
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geg: 01***********
Solution is combination of these schemas. Schema representsa particular component of solution.
30/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
Schema and HyperPlane
Schema - solution string with some blank fields
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geg: 01***********
Solution is combination of these schemas. Schema representsa particular component of solution.
Solution space : N-dimensional HyperCube
30/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
Schema and HyperPlane
Schema - solution string with some blank fields
![Page 121: genetic algorithm.pdf](https://reader030.vdocument.in/reader030/viewer/2022020714/577cd6cb1a28ab9e789d4403/html5/thumbnails/121.jpg)
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eg: 01***********
Solution is combination of these schemas. Schema representsa particular component of solution.
Solution space : N-dimensional HyperCube
Schema : HyperPlane
30/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
Schema and HyperPlane
Schema - solution string with some blank fields
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eg: 01***********
Solution is combination of these schemas. Schema representsa particular component of solution.
Solution space : N-dimensional HyperCubeSchema : HyperPlane
In 3D cube, 0** represent front face.
30/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
Schema and HyperPlane
Schema - solution string with some blank fields
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eg: 01***********
Solution is combination of these schemas. Schema representsa particular component of solution.
Solution space : N-dimensional HyperCubeSchema : HyperPlane
In 3D cube, 0** represent front face.
There is competition between Schema with n bit values insame positions.e g:- 00*, 01*, 10*, 11* are competing
Winner is the schema with highest fitness.
30/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
Implicit Parallelism
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A solution string belongs to many HyperPlanes (2N −1).eg: 010 belongs to 0** , *1*, **0
31/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
Implicit Parallelism
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A solution string belongs to many HyperPlanes (2N −1).eg: 010 belongs to 0** , *1*, **0
Single Evaluation of string leads to evaluation of different
hyperplanes in an implicitly parallel fashion (John Holland 1975
);
31/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
Implicit Parallelism
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A solution string belongs to many HyperPlanes (2N −1).eg: 010 belongs to 0** , *1*, **0
Single Evaluation of string leads to evaluation of different
hyperplanes in an implicitly parallel fashion (John Holland 1975
);Evaluation of population of strings, samples far morehyperplanes as compared to number of strings contained inthe population.
31/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
Implicit Parallelism
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A solution string belongs to many HyperPlanes (2N −1).eg: 010 belongs to 0** , *1*, **0
Single Evaluation of string leads to evaluation of differenthyperplanes in an implicitly parallel fashion (John Holland 1975 );
Evaluation of population of strings, samples far morehyperplanes as compared to number of strings contained inthe population.
These cumulative effects provides statistical information to
GA about any particular subset of hyperplanes.
31/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?Applications
Schema and HyperPlane
Implicit ParallelismThe Schema Theorem
The Schema Theorem
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32/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Schema and HyperPlaneImplicit ParallelismThe Schema Theorem
The Schema Theorem
The Schema Theorem (Holland 1992; Goldberg 1989)
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The Schema Theorem (Holland 1992; Goldberg 1989 ).It provides a lower bound on the change in the sample rate fora single hyperplane from generation t to generation t + 1.
32/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Schema and HyperPlaneImplicit ParallelismThe Schema Theorem
The Schema Theorem
The Schema Theorem (Holland 1992; Goldberg 1989)
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The Schema Theorem (Holland 1992; Goldberg 1989 ).It provides a lower bound on the change in the sample rate fora single hyperplane from generation t to generation t + 1.
Equation:
32/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Schema and HyperPlaneImplicit ParallelismThe Schema Theorem
The Schema Theorem
The Schema Theorem (Holland 1992; Goldberg 1989)
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The Schema Theorem (Holland 1992; Goldberg 1989 ).It provides a lower bound on the change in the sample rate fora single hyperplane from generation t to generation t + 1.
Equation:
Building Blocks Hypothesis (Holland, 1975; Gold-berg, 1989 )Low-order, highly-fit schemas recombine to form even betterschemas.
In Goldberg’s words, “we construct better and better stringsfrom the best partial solutions of past samplings”
32/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Advantages
Disadvantages
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WHY GA?
33/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Advantages
Disadvantages
Advantages
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Implicit Parallelism - Solution Space is explored in multipledirections (GoldBerg - GA in Search and Optimization)
34/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Advantages
Disadvantages
Advantages
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Implicit Parallelism - Solution Space is explored in multipledirections (GoldBerg - GA in Search and Optimization)
Nonlinear problems -Large Solution space, but GA areideal.(Forrest - 1993 Genetic Algorithm)
34/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Advantages
Disadvantages
Advantages
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Implicit Parallelism - Solution Space is explored in multipledirections (GoldBerg - GA in Search and Optimization)
Nonlinear problems -Large Solution space, but GA areideal.(Forrest - 1993 Genetic Algorithm)
Works on complex landscape (discontinuous, noisy, changingwith time) (John Koza - Genetic Programming IV 2004 )
34/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Advantages
Disadvantages
Advantages
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Dilemma of global optimum vs many local optima. GA strikeperfect balance (John Holland - Genetic Algorithm 1992 )
35/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Advantages
Disadvantages
Advantages
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Dilemma of global optimum vs many local optima. GA strikeperfect balance (John Holland - Genetic Algorithm 1992 )
GA can manipulate many parameters simultaneously (Forrest -
Genetic algorithms: principles of natural selection applied to computation.1993 )
35/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
TheoryWhy GA?
Applications
Advantages
Disadvantages
Advantages
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Dilemma of global optimum vs many local optima. GA strikeperfect balance (John Holland - Genetic Algorithm 1992 )
GA can manipulate many parameters simultaneously (Forrest -
Genetic algorithms: principles of natural selection applied to computation.1993 )
GA don’t have specific knowledge of problem. All possiblesearch pathways are considered in GA.(John Koza - Genetic
Programming III 1999 )
35/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
Advantages
Disadvantages
Disadvantages
Computationally expensive and time consuming
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Computationally expensive and time consuming
36/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
Advantages
Disadvantages
Disadvantages
Computationally expensive and time consuming
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Computationally expensive and time consuming
Issues in representation of problem
36/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
Advantages
Disadvantages
Disadvantages
Computationally expensive and time consuming
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Computationally expensive and time consuming
Issues in representation of problem
Proper writing of fitness function
36/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
Advantages
Disadvantages
Disadvantages
Computationally expensive and time consuming
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Computationally expensive and time consuming
Issues in representation of problem
Proper writing of fitness function
Proper values of size of population, crossover and mutationrate
36/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
Advantages
Disadvantages
Disadvantages
Computationally expensive and time consuming
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Computationally expensive and time consuming
Issues in representation of problem
Proper writing of fitness function
Proper values of size of population, crossover and mutationrate
Deceptive Fitness Function (Mitchell, Melanie 1996 )
36/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
Advantages
Disadvantages
Disadvantages
Computationally expensive and time consuming
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p y p g
Issues in representation of problem
Proper writing of fitness function
Proper values of size of population, crossover and mutationrate
Deceptive Fitness Function (Mitchell, Melanie 1996 )
Premature Convergence
36/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
Advantages
Disadvantages
Disadvantages
Computationally expensive and time consuming
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p y p g
Issues in representation of problem
Proper writing of fitness function
Proper values of size of population, crossover and mutationrate
Deceptive Fitness Function (Mitchell, Melanie 1996 )
Premature Convergence
No one mathematically perfect solution since problems of biological adaptation don’t have this issue.
36/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
Applications
Aeronautics
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APPLICATIONS
37/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
Applications
Aeronautics
Applications
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Image courtesy: http://www.google.com
38/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
Applications
Aeronautics
Aeronautics
Multiple-objective genetics algorithm to design wing shape for
supersonic aircraft
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39/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Aeronautics
Multiple-objective genetics algorithm to design wing shape for
supersonic aircraft
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Four major considerations for wing design
39/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Aeronautics
Multiple-objective genetics algorithm to design wing shape for
supersonic aircraftF j id i f i d i
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Four major considerations for wing design
Minimizing aerodynamic drag at supersonic cruising speeds
39/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Aeronautics
Multiple-objective genetics algorithm to design wing shape for
supersonic aircraftF j id i f i d i
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Four major considerations for wing design
Minimizing aerodynamic drag at supersonic cruising speedsMinimizing drag at subsonic speeds
39/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Aeronautics
Multiple-objective genetics algorithm to design wing shape for
supersonic aircraftF j id ti f i d i
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Four major considerations for wing design
Minimizing aerodynamic drag at supersonic cruising speedsMinimizing drag at subsonic speedsMinimizing aerodynamic load (bending force on wing)
39/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Aeronautics
Multiple-objective genetics algorithm to design wing shape for
supersonic aircraftF j id ti f i d i
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Four major considerations for wing design
Minimizing aerodynamic drag at supersonic cruising speedsMinimizing drag at subsonic speedsMinimizing aerodynamic load (bending force on wing)Minimizing twisting moment of wing
39/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Aeronautics
Multiple-objective genetics algorithm to design wing shape for
supersonic aircraftFour major considerations for wing design
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Four major considerations for wing design
Minimizing aerodynamic drag at supersonic cruising speedsMinimizing drag at subsonic speedsMinimizing aerodynamic load (bending force on wing)Minimizing twisting moment of wing
Objectives are mutually exclusive and optimizing themrequires tradeoff
39/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Aeronautics
Multiple-objective genetics algorithm to design wing shape for
supersonic aircraftFour major considerations for wing design
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Four major considerations for wing design
Minimizing aerodynamic drag at supersonic cruising speedsMinimizing drag at subsonic speedsMinimizing aerodynamic load (bending force on wing)
Minimizing twisting moment of wing
Objectives are mutually exclusive and optimizing themrequires tradeoff
Chromosomes - 66 real valued numbers, with population size -
64 and simulated for 70 generations.
39/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Aeronautics
Multiple-objective genetics algorithm to design wing shape for
supersonic aircraftFour major considerations for wing design
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Four major considerations for wing design
Minimizing aerodynamic drag at supersonic cruising speedsMinimizing drag at subsonic speedsMinimizing aerodynamic load (bending force on wing)
Minimizing twisting moment of wing
Objectives are mutually exclusive and optimizing themrequires tradeoff
Chromosomes - 66 real valued numbers, with population size -
64 and simulated for 70 generations.Evolved wing configurations outperformed existing humandesigned-wings
39/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
References
Obayashi, Shigeru, Daisuke Sasaki, Yukihiro Takeguchi, and NaokiHirose. “Multiobjective evolutionary computation for supersonicwing shape optimization ” IEEE Transactions on Evolutionary
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wing-shape optimization. IEEE Transactions on EvolutionaryComputation, vol.4, no.2, p.182-187 (July 2000).
Genetic Programming : On the Programming of Computers byMeans of Natural Selection by John R. Koza
http://www.myreaders.info/09 Genetic Algorithms.pdf
http://www.obitko.com/tutorials/genetic-algorithms/search-space.php
http://www.talkorigins.org/faqs/genalg/genalg.html
http://en.wikipedia.org/wiki/Genetic algorithm
http://brainz.org/15-real-world-applications-genetic-algorithms/
40/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Conclusion
Large Appeal of Genetic Algorithms
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41/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Conclusion
Large Appeal of Genetic Algorithms
Is it because of Performance?
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41/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Conclusion
Large Appeal of Genetic Algorithms
Is it because of Performance?Or is it Aesthetic pleasing origins in theory of evolution ?
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p g g y
41/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Conclusion
Large Appeal of Genetic Algorithms
Is it because of Performance?Or is it Aesthetic pleasing origins in theory of evolution ?
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41/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm
IntroductionAlgorithm
Theory
Why GA?Applications
ApplicationsAeronautics
Questions
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42/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm